The person who is "one call away" is saying that they are very near, and readily available to the caller.
Not only is the person suggesting they are very near, but that they are capable of doing great things, comparing themselves to Superman (which is definitely a hyperbole).
As for using the saying, "got nothing on me," It's not something we would use often, but is still commonly understood to mean that "I'm just as good at them," or "they are not any better than me at such and such."
Hope that helps,
Merrit